The problem of optimizing trajectories in the three-body problem, or even the n-body problem, for n=3, 4, has been addressed in many papers throughout the years. If one had a trajectory that started from a given position and it was desired to optimize it by minimizing the maneuvers, DV, along the trajectory, the field of optimal control theory has many approaches to this problem.
The previous ways transfers were designed to Earth-Moon Lagrange point L2 from parking orbits about the Earth, without the use of optimization methods using low energy orbits on the stable manifold to Lagrange point L2 orbit and not for hybrid spacecraft with two different types of engines, is to simply do a standard differential targeting from the parking orbit, using a first maneuver to get to the beginning of the stable manifold and to a given orbit and apply a second maneuver at the stable manifold orbit to get to the Lagrange point L2 orbit. This transfer to Lagrange point L2 orbit using the two maneuvers is found with standard ‘differential targeting’ together with use of a stable manifold. With such a method of determining the transfer to Lagrange point L2 orbit, one could apply a local optimizer just valid at the specific maneuver points, which is only valid for chemical/impulsive maneuvers and is not valid for hybrid spacecraft. In another method the transfer to Lagrange point L2 orbit may be determined using low thrust only or impulsive thrust only however, the low thrust only or impulsive thrust only method is not valid for hybrid spacecraft.
Low-energy Earth-Moon transfers with longer flight times of 90 days are also used for the transfer to Lagrange point L2 orbit (e.g. GRAIL mission). However, these a low energy solutions for transfer to Lagrange point L2 orbit utilize an exterior ballistic capture transfer with a flight time of 90-150 days and are not relevant to transfers having flight times around 6 days.